Ogle, Welcome you will find that being a quilter is like being a small child - you are always wanting to try new things and learn new things. Part of being a quilter is stepping outside of the box (we have all done this), and for some of us that's why we are quilters because we have always seen and done things outside of the box.
As far as your question about using your batting as the backing of your quilt goes. If the quilt is only an fiber art piece, not to be used or washed a lot. Then sure you can, look at all the pictures of fiber art work that shown in museums. But if your wanting to use the quilt or give it as a gift to be used, you will need a fabric backing. Batting is made to be inside (sandwiched between fabrics).
Good luck with what you decide to do, please post pictures when your finished.